WASHINGTON — Top congressional leaders emerged from a meeting with President Obama at the White House on Friday trying to project bipartisan confidence that they would break through gridlock to avert a potential economic catastrophe triggered by budget cuts and increased taxes.

Following an hourlong meeting at the White House, the four top congressional leaders stood by one another outside the West Wing, taking turns calling the meeting “very constructive.” Stocks on Wall Street briefly surged, with renewed optimism that a chief economic roadblock would be removed.

“It was good,” said House minority leader Nancy Pelosi. “I feel confident that a solution may be in sight.”

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Both sides seem to be looking at the same roadmap — Republicans now concede that they will agree to increase tax revenues, and Democrats say they will agree to more spending cuts — but they are still divided over which route to take.

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And despite the show of solidarity, no substantive progress was revealed after the meeting. Major disagreements center on whether tax rates will rise for the wealthiest Americans. Obama has insisted that he wants rates for families making $250,000 or more to return to Clinton-era levels, which means they would go from 35 percent to 39.6 percent. Republicans have adamantly opposed any changes to the rates, saying they instead want to close loopholes or limit tax deductions to raise revenues.

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Congressional aides will now turn to the difficult task of trying to hammer out a deal. Obama is heading out on a four-day diplomatic trip to Asia on Saturday, and Congress is in recess next week. But negotiators plan to meet through the week, and Pelosi said a deal should be in place before Christmas.

The session was the first time in six months that all four leaders had gathered at the White House. House Speaker John Boehner said that he presented a “framework” that would both cut spending and reform the tax code.

“To show our seriousness, we’ve put revenue on the table as long as it’s accompanied by significant spending cuts,” said Boehner, an Ohio Republican.

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An aide later said that Boehner called for tax and entitlement reform to be tackled over the next year, since the issues are too complex to solve over the course of the next few weeks. Instead, he wants the initial agreement to include specific targets for savings and for tax reform changes, with details to be worked out in 2013. That approach is similar to a two-step process Obama outlined at his press conference Wednesday.

If no deal is made by the end of the year, tax rates for everyone will increase to the levels they were about a decade ago, before President George W. Bush signed a series of tax cuts. At around the same time, cuts in federal spending, including the military, will be enacted as part of Congress’s budget deal in 2011.

Economists contend such a one-two combination would send the soft economy reeling, leading to job losses and drops in consumer and business spending. The effect would be felt throughout the nation.

Massachusetts officials estimate that state tax collections alone could decline by $300 million in the first six months of 2013 and another $1 billion in the fiscal year beginning July 2013. Spending cuts would strip away millions of dollars in grant funding for local communities — in the middle of their current fiscal years — with no way to make it up.

Those initial grant cuts for Massachusetts communities include $18.2 million for schools, $21.2 million for special education, $7.3 million for community development block grants, and $11.2 million for LIHEAP, the federal heating fuel assistance program for low- and middle-income families.

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The state’s private-sector economy also would suffer from a reduction of about $1.5 billion in defense and health spending, according to state estimates.

Lieutenant Governor Timothy Murray met with city and town officials this week and discussed the potential consequences.

“It would have a pretty devastating impact, really across the board,’’ Murray said Friday in a phone interview.

In the aftermath of the election, both sides have been posturing and outlining their own prebargaining positions. Obama has demanded that any deal include $1.6 trillion in tax increases for the wealthiest Americans, something Republicans oppose.

Republicans say they are willing to make tax code changes that would result in higher payments for the wealthy, but they are more focused on cutting costs among the large entitlement programs such as Medicare, Medicaid, and Social Security.

But at least for one day, a sense of solidarity replaced the bitter divisiveness that broke into the open during the last round of fiscal talks in 2011.

A few seconds later, Pelosi, too, declared, “It was a very constructive meeting.”

Speaking last, Senate minority leader Mitch McConnell said, “I can only echo the observations of the other leaders that it was a constructive meeting.”

White House spokesman Jay Carney later released a statement saying it was a “constructive meeting” and added, “we will continue a constructive process.”

Outside observers say there is reason for optimism.

“Should we be concerned? Yes,” said Cornelius Hurley, director of the Morin Center for Banking and Financial Law at Boston University. “But I’m a lot more confident now than I was in the midst of the 2011 debacle that they will get to a resolution.”

The negotiations could set the tenor for the start of Obama’s second term. They could signal months of acrimony or set the stage for a series of bipartisan agreements. Republicans lost seats in the House and Senate and were unable to win the White House. But they still control the House and have the numbers needed to stop legislation in the Senate.

Obama has been more assertive than he was in past negotiations, pledging that he would not agree to any deal that allows tax rates for the wealthy to stay as they are. He is also preparing to take his campaign outside Washington in the coming weeks, trying to use his election win as a rallying cry.

“That’s an agenda that Democrats and Republicans and independents, people all across the country share,” Obama said at the beginning of the Friday meeting. “So our challenge is to make sure that we are able to cooperate together, work together, find some common ground, make some tough compromises, build some consensus, and to do the people’s business.”

Just as the meeting began, when reporters were ushered in for photos, Obama remarked playfully that Boehner’s birthday is Saturday.

“We didn’t make him a cake because we didn’t know how many candles we’d need,” Obama said.

As they laughed and shook hands, Boehner, who is turning 63, said, “Yeah, right.”

Obama later gave Boehner a bottle of Tuscan red wine. The bottle of 1997 Poggio Antico Brunello di Montalcino Altero retails for about $125.